The classical Shannon sampling theorem states that a signal f with Fourier transform F ∈ L(R) having its support contained in (−π, π) can be recovered from the sequence of samples (f(n))n∈Z via f(t) = ∑ n∈Z f(n) sin(π(t− n)) π(t− n) (t ∈ R). In this article we prove a generalization of this result under the assumption that F ∈ E (R) has support contained in (−π, π).

In this article we study the existence of almost periodic solutions for distributed parameters biochemical system, with time delay when the input Sin is time dependent. This study is motivated by the input begin time dependent in many applications, and by the importance of almost periodically varying environments. Using the semigroup method, we prove that if the input is almost periodic then th...

The septation initiation network (SIN) regulates aspects of cell growth and division in Schizosaccharomyces pombe and is essential for cytokinesis. Insufficient signalling results in improper assembly of the contractile ring and failure of cytokinesis, generating multinucleated cells, whereas too much SIN signalling uncouples cytokinesis from the rest of the cell cycle. SIN signalling is theref...

A common objection to “sin taxes”—corrective taxes on goods like cigarettes, alcohol, and sugary drinks, which are believed to be over-consumed—is that they fall disproportionately on low-income consumers. This paper studies the interaction between corrective and redistributive motives in a general optimal taxation framework. On the one hand, redistributive concerns amplify the corrective benef...

A graph   is called integral if all eigenvalues of its adjacency matrix  are integers.  Given a subset $S$ of a finite group $G$, the bi-Cayley graph $BCay(G,S)$ is a graph with vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid sin S, xin G}$.  In this paper, we classify all finite groups admitting a connected cubic integral bi-Cayley graph.

The time-dependent CP asymmetries in fully reconstructed B0→D(∗)±π∓/ρ∓ decays (new preliminary result), and in partially reconstructed B0→D(∗)±π∓ decays, are measured with the BABAR detector at the PEP-II asymmetric B factory at SLAC, using 232 million Υ (4S) → BB decays. We combine the above results and, using other measurements and theoretical assumptions, we interpret them in terms of the an...

Some facts about sines and cosines: • cos(A+B) = cos(A) cos(B)− sin(A) sin(B) • sin(A+B) = sin(A) cos(B) + cos(A) sin(B) • Cosine is an even function: cos(−θ) = cos(θ) • Sine is an odd function: sin(−θ) = − sin(θ) • cos(ωt− π/2) = sin(ωt) • R cos(ωt + φ) = R sin(φ) cos(ωt) + R cos(φ) sin(ωt), and any wave form can be written as a linear combination of sines and cosines. Similarly, A sin(ωt) +B ...

Measurements of sin 2β at BABAR with charmonium and penguin decays. Abstract This article summarises measurements of time-dependent CP asymmetries in decays of neutral B mesons to charmonium, open-charm and gluonic penguin-dominated charmless final states. Unless otherwise stated, these measurements are based on a sample of approximately 230 million Υ (4S)→ BB decays collected by the BABAR dete...

we show that the lattice of all ideals of a ring $r$ can be embedded in the lattice of all its fuzzyideals in uncountably many ways. for this purpose, we introduce the concept of the generalizedcharacteristic function $chi _{s}^{r} (a)$ of a subset $a$ of a ring $r$ forfixed $r , sin [0,1] $ and show that $a$ is an ideal of $r$ if, and only if, its generalizedcharacteristic function $chi _{s}^{...